[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

Vision System for Group of Mobile Robots 149
smaller than minimal width or height of objects of interest. The implementation
presented above additionally presumes that input image consists of two values
only: 0 for background and 255 for foreground objects.
2.7 Estimation of Object’s Position and Orientation
Vision algorithm is capable of precise estimation of position of all robots and ball
and orientation of robots only. (Quite naturally, orientation is not calculated for
a ball). Robots could be interpreted as agents and the approach of planning could
be used [9]. However , real time applications requires fast adaptation to changes.
Therefore different approach was used. The method used here is described in more
detail in [16]. Calculations are done in four stages. First, for each object, the following
integrals are calculated:
(16)
(17)
(18)
Where is a region occupied by the object, is its area and and are static
moments. Next, the position of each object is found from the formulas describing
center of the mass:
(19)
Then the angle of main axis of inertia is calculated for each robot and finally, the
direction of this axis is chosen, as the algorithm for finding the angle of main axis
of inertia can’t do that automatically and additional heuristics is needed. These
two stages are described in more detail in sections below.
2.8 Angle of Main Axis of Inertia
Estimating the orientation of robot on the basis of main axis of inertia is possible
thanks to the special shape of the color marker placed on the top of each robot.
The shape is presented on Figure 6.
(20)